Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}3x+2y &= -9 \\ -4x-y &= 5\end{align*}$
Solution: Begin by moving the $x$ -term in the second equation to the right side of the equation. $-y = 4x+5$ Divide both sides by $-1$ to isolate $y$ $y = {-4x - 5}$ Substitute this expression for $y$ in the first equation. $3x+2({-4x - 5}) = -9$ $3x - 8x - 10 = -9$ Simplify by combining terms, then solve for $x$ $-5x - 10 = -9$ $-5x = 1$ $x = -\dfrac{1}{5}$ Substitute $-\dfrac{1}{5}$ for $x$ back into the top equation. $3( -\dfrac{1}{5})+2y = -9$ $-\dfrac{3}{5}+2y = -9$ $2y = -\dfrac{42}{5}$ $y = -\dfrac{21}{5}$ The solution is $\enspace x = -\dfrac{1}{5}, \enspace y = -\dfrac{21}{5}$.